On the numerical solution of a logarithmic integral equation of the first kind for the Helmholtz equation.

We describe a quadrature method for the numerical solution of the logarithmic integral equation of the first kind arising from the single-layer approach to the Dirichlet problem for the two-dimensional Helmholtz equation in smooth domains. We develop an error analysis in a Sobolev space setting and prove fast convergence rates for smooth boundary data. [ABSTRACT FROM AUTHOR]